Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations; (2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates; (3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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降阶识别方法：分层算法或变量消除算法


降阶识别算法通常用于机器学习和大数据技术，这些技术广泛存在大规模系统。对于大规模系统识别，传统的最小二乘算法涉及高阶矩阵逆计算，而传统的梯度下降算法收敛速度较慢。本文提出的降阶算法与以前的工作相比具有一些优势：（1）通过对参数向量的顺序划分，可以将高阶矩阵的逆计算简化为低阶矩阵逆计算;（2） 具有比梯度下降算法更好的条件信息矩阵，因此具有更快的收敛速率;（3） 使用 Aitken 加速方法可以提高其收敛速率，因此基于降阶的 Aitken 算法至少是二次收敛的，对步长没有限制。还给出了降阶算法的属性。仿真结果验证了所提算法的有效性。